I am on dialysis and am fluid restricted. I find chewing ice is one way to get the fluids I need and not "over do it" on water consumption.
Plus, keeping a cool mouth can't help but be good for you. If oral micro-organisms aren't frozen to death by the ice, at least in a cold state they don't reproduce nearly as fast.
Anemia? I don't know. I've had a hemoglobin of 6.5 all the way up to a hemoglobin of 14, and I have noticed no difference in "craving" for ice.

Hi, Morlock! Sorry for the somewhat late response, but I found your comment to be pretty interesting. I, myself, am not dialysis but my grandfather has kidney issues. Currently, they're investigating whether or not he should do dialysis or if they should do a full blown kidney transplant. Regardless of what the doctors decide, we were both curious about the fluid intake aspect of kidney issues. My grandfather wasn't necessarily told to limit fluid intake, but we're wondering if he should limit fluid intake anyway. Also, if he DOES go through with a transplant, is limited fluid intake still imperative? Clearly you haven't had a transplant, but maybe you have information that we don't necessarily have.

Either way, chewing on ice is an interesting way of cooling the mouth and throat without taking in too many fluids. The next time I bring my grandpa in for his exam (which should be today), I'll bring this comment up. Thanks! =)